Description Usage Arguments Details Value Author(s) References See Also Examples
wfgl
estimates joint partial correlation matrices from two multivariate
normal distributed datasets using an ADMM based algorithm. Allows for paired data.
1 2 3 4 5 | wfgl(D1, D2, lambda1, lambda2, paired = TRUE, automLambdas = TRUE,
sigmaEstimate = "CRmad", pairedEst = "Reg-based-sim", maxiter = 30,
tol = 1e-05, nsubset = 10000, weights = c(1,1), rho = 1, rho.increment = 1,
triangleCorrection = TRUE, alphaTri = 0.01, temporalFolders = FALSE,
notOnlyLambda2 = TRUE, roundDec = 16, burn = 0, lambda1B = NULL, lambda2B = NULL)
|
D1 |
first population dataset in matrix n_1 \times p form. |
D2 |
second population dataset in matrix n_2 \times p form. |
lambda1 |
tuning parameter for sparsity in the precision matrices (sequence of lambda1 is allowed). |
lambda2 |
tuning parameter for similarity between the precision matrices in the two populations (only one value allowed at a time). |
paired |
if |
automLambdas |
if |
sigmaEstimate |
robust method used to estimate the variance of estimated partial correlations: name that uniquely identifies
|
pairedEst |
type of estimator for the correlation of estimated partial correlation coefficients when |
maxiter |
maximum number of iterations for the ADMM algorithm. |
tol |
convergence tolerance |
nsubset |
maximum number of estimated partial correlation coefficients (chosen randomly) used to select |
weights |
weights for the two populations to find the inverse covariance matrices. |
rho |
regularization parameter used to compute matrix inverse by eigen value decomposition (default of 1). |
rho.increment |
default of 1. |
triangleCorrection |
if |
alphaTri |
significance level for the tested triangle graph structures. |
temporalFolders |
if |
notOnlyLambda2 |
if |
roundDec |
number of decimals to be stored, if low it reduces de memory space used. |
burn |
initial number of iterations which consider the original interpretation of lambda1 (given by |
lambda1B |
lambda1 interpreted as when |
lambda2B |
lambda2 interpreted as when |
wfgl
uses a weighted-fused graphical lasso maximum likelihood estimator by solving:
\hat{Ω}_{WFGL}^{λ} = \arg\max\limits_{Ω_X,Ω_Y} [∑_{k=X,Y} \log\detΩ_k -tr(Ω_k S_k) - P_{λ_1,λ_2,V}(Ω_X,Ω_Y)],
with
P_{λ_1,λ_2, V}(Ω_X,Ω_Y) = λ_1||Ω_X||_1 + λ_1||Ω_Y||_1 +λ_2∑_{i,j} v_{ij} |Ω_{Y_{ij}}-Ω_{X_{ij}}|,
where λ_1 is the sparsity tuning parameter, λ_2 is the similarity tuning parameter, and V = [v_{ij}]
is a p\times p matrix to weight λ_2 for each coefficient of the differential precision matrix.
If datasets are independent (paired = "FALSE"
), then it is assumed that v_{ij} = 1 for all pairs (i,j).
Otherwise (paired = "TRUE"
), weights are estimated in order to account for the dependence structure between datasets in the differential
network estimation.
Lambdas can be estimated in each iteration by controlling the expected false positive rate (EFPR) in
case automLambdas = TRUE
. This transforms the problem of selecting the tuning parameters λ_1 and λ_2 to the
selection of the desired EFPR. In case lambda2
is a single value and lambda1
is a vector with several values, then lambda selection
approaches implemented at lambdaSelection
can also be used.
If triangleCorrection = TRUE
, the weakest edges of estimated triangular motifs are further tested. The reason is that edges that complete
triangular graph structures suffer an overestimation when applying the ADMM due to using regularized inverse procedures.
An object of class wfgl
containing the following components:
path |
adjacency matrices. |
omega |
precision matrices. |
triangleCorrection |
determines if triangle structures are tested. |
weakTriangEdges |
weakest edges in triangle structures which have been tested. |
weakTriangEdgesPval |
p-values for the weakest edge in triangle structures. |
diff_value |
convergence control. |
iters |
number of iterations used. |
corEst |
dependence structure estimated measure used in the estimation to account for dependent datasets. |
Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.
Danaher, P., P. Wang, and D. Witten (2014). The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) (2006), 1-20.
Boyd, S. (2010). Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning 3(1), 1-122.
plot.wfgl
for graphical representation.
wfrl
for weighted fused regression lasso.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
# example to use of wfgl
EX2 <- pcorSimulatorJoint(nobs =50, nclusters = 3, nnodesxcluster = c(30, 30,30),
pattern = "pow", diffType = "cluster", dataDepend = "diag",
low.strength = 0.5, sup.strength = 0.9, pdiff = 0.5, nhubs = 5,
degree.hubs = 20, nOtherEdges = 30, alpha = 2.3, plus = 0,
prob = 0.05, perturb.clust = 0.2, mu = 0, diagCCtype = "dicot",
diagNZ.strength = 0.6, mixProb = 0.5, probSign = 0.7,
exactZeroTh = 0.05)
## not run
#wfgl1 <- wfgl(EX2$D1, EX2$D2, lambda1 = 0.05, lambda2 = 0.1, paired = TRUE,
# automLambdas = TRUE, sigmaEstimate = "CRmad", pairedEst = "Reg-based-sim",
# maxiter = 30)
#print(wfgl1)
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